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Regularity of Diophantine quadruples over ℚ(i)[X]

2026/07/30 by Sanda Bujačić Babić, Ana Jurasić
Mathematics · #math.NT #msc:11D09 #msc:11D45

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arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We prove that every Diophantine quadruple \a,b,c,d\ over ℚ(i)[X] that contains at least one non-constant polynomial is regular; that is, (a+b-c-d)2=4(ab+1)(cd+1). This result is consistent with the corresponding results over ℤ[i][X] and ℝ[X], but contrasts with the situation over ℂ[X].

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